Lawn Tractor Craftsman 17.5hp B/S Motor Model #247.288810

Mower went slower, and slower thought it was running out of fuel, stopped, and shut engine off added fuel tried to start, it would idle for a few seconds then stop with throttle wide open, I can try starting again it would click a few times then turn over, samething some times it will idle, sometimes not? Can only do this a few times then starter becomes hot, and won't turn over.

Things I have done, Checked all safety's, New battery, New fuel filter, new 20amp fuse, Checked back fire solenoid on bottom of bowl it worked ok when I turned key on, and off, cleaned carb, checked fuel line good flow to carb, but I think its just not getting the fuel it needs I just don't know! I think I have more than 1 problem, maybe starter switch, starter solenoid,and not getting fuel.
Help. Thank you for any advice at this time just banging my head One more thing my wife was mowing while I was at work

 

connect a new spark plug, don't put it in, hold it against a metal part of the engine, turn the key for just a second to see if there is a spark then install it. What year is the mower, and whats the name of the engine? Usually spark, gas and air is all you need. As long as your starter is turning the engine, there is no problem there. Try starting with the gas cap off the tank as well.

 

And what do you consider "I cleaned the carburetor?
Did you take it completely apart and soak it in cleaner? Or just blow some air in it?
Have you removed the fuel bowl and lifted and lowered the float to see if it's starting and completely stopping the fuel flow.
Does this mower have a fuel pump? If so have you disconnect the fuel line to the carb. and turned the key to see if it's pumping?

 

Yes to all.
Took carb apart checked float, cleaned with cleaner. No fuel pump. I also took the Idle mixture needle out cleaned, and replaced. Thank you!

 

2011 Briggs, and Stratton 17.5 Checked on motor, now obsolete.
and yes I did check for spark with plug removed good spark with old,and new plug, and I know about the vented gas cap for positive pressure, but I have not tried that I will, and will reply back, by tomorrow thank you.